1. **State the problem:** Find three numbers that lie between $\frac{\pi}{2}$ and $\sqrt{48}$ on the number line. 2. **Calculate approximate values:** - $\frac{\pi}{2} \approx \frac{3.1416}{2} = 1.5708$ - $\sqrt{48} = \sqrt{16 \times 3} = 4 \sqrt{3} \approx 4 \times 1.732 = 6.928$ 3. **Interpretation:** We want numbers between approximately $1.5708$ and $6.928$. 4. **Select numbers:** Any numbers greater than $1.5708$ and less than $6.928$ qualify. 5. **Example numbers:** $2$, $3$, and $5$. **Final answer:** The numbers $2$, $3$, and $5$ lie between $\frac{\pi}{2}$ and $\sqrt{48}$ on the number line.